Use Logarithmic Differentiation to Find the Derivative of the Function $y=\sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$

question 142

Multiple Choice

Use logarithmic differentiation to find the derivative of the function. $y=\sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$

• A) \(y^{\prime}=-\frac{9 x}{\left(x^{4}-1\right)} \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}\)
• B) \(y^{\prime}=\frac{9 x}{4 x^{4}-1} \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}\)
• C) \(y^{\prime}=-\frac{36 x}{x^{4}-1} \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}\)
• D) \(y^{\prime}=-\frac{36 x}{x^{4}-1}\)
• E) \(y^{\prime}=-\frac{4 x}{9\left(x^{4}-1\right)} \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}\)

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